An active investor plays some role in the ongoing business, in addition to investing cash into the business. It could be that they are an advisor to the company, either formally or informally. It could be that they sit on the board of directors. Or it could be that they are involved as a part-time or full-time employee with the company, even to the point of being considered a partner in the business.
The opposite is a passive investor. Most equity investors have in mind to be either active or passive. Some active investors including many venture capitalists balance active investments, which take a great deal of time, with some passive investments, where they trust the other investors to act on their behalf.
See Fred Wilson’s blog post “Active and Passive Investing” for further perspective.