I have been pondering the question of what philosophy is and what it aims to achieve. One idea that came to mind is that philosophy might consist in defining the being of each thing. In other words, philosophy might be concerned with understanding the essence or nature of things, and providing definitions or explanations of what they are. Is this an accurate understanding of what philosophy is, or is there more to it than this?
No. There is a subdiscipline in philosophy called ontology, which deals with the nature of being. But "defining the being of each thing" already presupposes a series of things that are challenged by some philosphers and philosophies.
You might like this answer, which relates to your topic: (Why) is this negative outlook on the concept of philosophy misguided?
What exactly philosophy is is a matter of philosophical contention. I recommend An Introduction to Metaphilosophy (GB) for an overview of various claims about what philosophy is. There's not always agreement about what philosophy is or what it does, and a surprising number of scientific intellectuals often display an general ignorance of the topic.
While it's tough to sum up the work above in a post, we can take a look at what amounts to broad consensus and define philosophy tentatively by it's subdisciplines. Philosophers, particularly living professional ones, often specialize in an area such as epistemology or logic, or generally several interrelated disciplines such as philosophy of mind and language. Some ideas important to philosophy are:
- Metaphysics: from WP:
Metaphysics is the branch of philosophy that studies the fundamental nature of reality. This includes the first principles of: being or existence, identity, change, space and time, cause and effect, necessity, actuality, and possibility.
- Epistemology: from WP:
Epistemology (/ɪˌpɪstəˈmɒlədʒi/ (listen); from Ancient Greek ἐπιστήμη (epistḗmē) 'knowledge', and -logy) is the branch of philosophy concerned with knowledge, and is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Epistemologists study the nature, origin, and scope of knowledge, epistemic justification, the rationality of belief, and various related issues.
- Ontology: from WP:
In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality... Ontology addresses questions like how entities are grouped into categories and which of these entities exist on the most fundamental level. Ontologists often try to determine what the categories or highest kinds are and how they form a system of categories that encompasses the classification of all entities. Commonly proposed categories include substances, properties, relations, states of affairs, and events.
- Axiology: from WP:
Axiology (from Greek ἀξία, axia: "value, worth"; and -λογία, -logia: "study of") is the philosophical study of value. It includes questions about the nature and classification of values and about what kinds of things have value. It is intimately connected with various other philosophical fields that crucially depend on the notion of value, like ethics, aesthetics or philosophy of religion. It is also closely related to value theory and meta-ethics. The term was first used by Eduard von Hartmann in 1887 and by Paul Lapie in 1902.
- Aesthetics: from WP:
Aesthetics (also esthetics) is the branch of philosophy concerned with the nature of beauty and the nature of taste; and functions as the philosophy of art. Aesthetics examines the philosophy of aesthetic value, which is determined by critical judgements of artistic taste; thus, the function of aesthetics is the "critical reflection on art, culture and nature"
- Ethics: from WP:
Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and wrong behavior". The field of ethics, along with aesthetics, concerns matters of value; these fields comprise the branch of philosophy called axiology.
- Logic: from WP:
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory.
- Metaphilosophy: from WP:
Metaphilosophy, sometimes called the philosophy of philosophy, is "the investigation of the nature of philosophy".... Its subject matter includes the aims of philosophy, the boundaries of philosophy, and its methods.
In general, philosophy is a sustained, systematic inquiry into an area of understanding that is currently outside the realm of common, widely accepted, confirmed knowledge and beliefs. The philosopher is an explorer at the edges of human thought.
As they pass into the mainstream, things that start as philosophies can become sciences, religions, aesthetics, methods, or any of the other things that are learned by transmission and not by inspiration.
The particular branch of philosophy concerned with the existence and nature of things is (as mentioned by @CriglCragl) called ontology.
The branch of philosophy that deals with applied reasoning is called "logic" and is generally considered to have passed over into the realm of science.
No, your definition is too narrow and would apply only to a small sub-set of what is considered to be philosophy. I suggest you search online for a list of topics that fall within the scope of philosophy, and you will readily see how few of them can be satisfactorily summed up by your suggested definition.