An expense is an additional cost on top of your work. Typical expenses are travel, hotel, meetings, lunch, merchandise, apps used, external help, etc. They can be internal or client-related.

When creating an expense you can set the date, add notes, associate it with a client and a project, and set tags. There's also the option to set markups, taxes and the person it will be reimbursed to.
Expenses can be added in a simple view like below:

Or in a bulk mode that can be used to add multiple expenses for multiple clients at once:

Tags are useful when filtering expenses because you can get a list of expenses and their total based on those tags. You can manage them by clicking on your profile picture (bottom left corner) → Company Settings → Project Accounting → Expenses Tags.
