What is Fat?
The gain in muscle weight is the same whether you are simultaneously losing fat or not. There is actually quite a bit of controversy regarding exactly how muscle gains take place. Water can be a factor for a number of reasons - for example, when you train your muscles they begin to hold more glycogen, which is stored carbohydrate - this enters the cell in a ratio of about 1 gram of carbohydrate to 2 - 4 grams of water, so there is substantial water involved. Creatine can also drive water into the cell.
Because this is not "water retention" i.e. water under the surface of the skin or external to the cells, but is in fact intracellular water, it is not necessarily a bad thing ... a volumized muscle cell (one expanded due to water content) may actually create an environment that caters to muscle growth and can provide more leverage which translates to strength.
You will gain strength and not necessarily muscle as well. This is because your muscles are made of motor units. These are bundles of muscle cells that are triggered by a single nerve, so they can either completely contract or not at all - there is no partial contraction. So lifting a heavier weight is simply a function of "recruiting" or causing more motor units to contract at once. Your muscle never utilizes all motor units and never coordinates them 100% efficiently. Therefore, as you train, your central nervous system (CNS) can become more effective at coordinating and recruiting these existing motor units, which means you can gain strength without necessarily gaining size.
Size often DOES come as the result of training, especially for someone who just begins. There is definitely an increased volume of muscle fibers - in other words, they increase in cross-section which creates overall size and improves the amount of leverage and force that the muscle can generate. So while strength and muscle aren't directly correlated, there IS a relationship. There is also a predominant belief that you have what are known as satellite cells - essentially muscle fibers that don't serve a specific function, but when you invoke the appropriate training, can fuse and turn into more force-generating muscle cells (there are various types of muscle fibers, and some can handle low force output but high volume, i.e. endurance, while others can generate massive force but are easily damaged and...