Q:

what does "great dedication" mean?

One action that strongly increased our conversion rate was studying the competition with great dedication.

I know the meaning of dedication, but here I think it has another meaning. 
dedication means   committed to a task or purpose.

A:

Great means "very much" or "intense".
Dedicate has multiple meanings.  It can mean

to memorialize or commemorate someone/something along with the creation of a new building or other artistic work - We dedicate this work to our late grandfather ... I dedicate this book to my wife ...
to exist or focus only towards the furtherance of a specific goal - This printer is dedicated to invoices, but the other printers can be used to print anything.
to concentrate available resources toward a specific goal, with the implication that such resources won't be available for other uses - Let's dedicate $20,000 to the new project.

In this case, the third meaning above applies.

