Basal insulin is given to match your liver's normal secretion of sugar throughout the day and night. When this is spot on you will have a blood sugar of 4.6 day and night provided you don't eat anything or exercise vigorously. This is "perfection" of course and what you are doing is doing what you can to approximate this. About half of the population have a dawn phenomenon which raises the morning blood sugars for a few hours. Even non diabetics have a dawn phenomenon.
Bolus insulin means a dose of insulin delivered in one go under the skin. To bolus 10 units is to give yourself a dose of ten units. In pumps you can give this as a square wave or dual wave or single bolus. In this way you determine the length of time over which it will be released. Bolusing your insulin simply means giving your insulin and can apply to basals or meal insulins.
Some people say "bolus insulin" when they are talking about delivering the insulin dose for their meals or for correction doses and don't intend for it to refer to basal insulin. This can sometimes cause confusion.
