When you are a beginner, the flute just sounds like a flute and it takes time for your hearing to be able to discern subtle differences. You can obviously hear the differences between high and low or loud and soft. But at these extremes there are also qualities which we describe as "colour". For example low notes where the air stream is slower and the lips more open tend to sound more fluffy, airy and with a diffuse quality; what could be called warm or breathy. Top register notes where the lips are more closed and the air stream is faster can be called brighter, more hard and edgy. Some teachers ascribe actual colours to these sounds; "smokey grey", "rich red velvet", "bright yellow" etc.
As you develop more control of your embouchure and breath you will be able to carry the soft and warm quality of the sound in the low register further up into the middle and high registers. Also you will gradually learn how to continue the clear and focused sound of the top register into the low register. Along with this improved technical skill your ability to hear subtle differences in tone qualities will improve.
Another ingredient of tone colour is vibrato which you need to be able to control and vary. (See chapter X, page x)
The main purpose of vibrato is to make the sound more interesting and to highlight and to draw attention to the important notes. Too constant and unvarying a vibrato quickly becomes boring so you need to decide when to use vibrato and when to play with a straighter sound. An intense vibrato can help to make loud dynamics seem even louder and therefore help your sound project, but again, it can sound boring if over-used. The flute sound which was the dominant style of playing from about 1950 to 1990 is often described as a "rich" tone colour. It has an obvious vibrato, quite wide and fast, along with an edgy tone production. Since then there has been a move away from this style. Vibrato is an important technique but must be used with care.
So to sum up, tone colour is a combination of the amount of air you use, how you direct that air, plus the speed and width of vibrato.