To understand the word "traction", think of a car that's driving in slippery mud. The wheels of the car might spin without moving the car forward. In this situation, you would say that the wheels "have no traction".

When people use the word "traction" to talk about a business, they mean the ability of the business to gain customers. So this sentence:

We're starting to gain traction.

...means that the business is starting to become popular and get customers.