Based on the nature of their growth, financial investments are divided into asset classes:
Equity: Investors directly, or indirectly (via a mutual fund), own a share (equity) of a company and expect their investment to appreciate as the value of the company grows.
Fixed Income: Investors directly, or indirectly (via a mutual fund), lend money to a company (or bank, or government) and expect to get a fixed rate of return.
Cash or equivalent: Money is kept either as currency, in a savings account, or given as a low return loan with high liquidity. Investors expect very little return but safety of capital with quick and easy access to their money.
As you can see, the amount and the way in which your money grows in these investments is very different. Your investment is an asset you have, therefore these are called asset classes.
Investments in these can be further divided into smaller groupings, once again based on their nature of growth.
So, Equity investments can be grouped by the size of company (large, mid, small); or market (Indian, US) etc.
These are called sub-asset classes and help portfolio managers target their investments better.
Note: As you can imagine, as you go deeper, more such groupings can be created using different dimensions and these tend to get non-standard very fast.