Analogous (analogous means similar) estimating is a kind of a ballpark estimate that takes into consideration previous similar projects when it comes to assessing how much time or money is needed to complete a project.
For example, let's say that a previous project consisted for creating a LAN for a small school, while your current project is to create a LAN for a large school, about 4 times the size of the small school. Since your LAN project on the smaller school had a total cost of $100,000 and a total duration of 2 months, then, if we apply Analogous estimation, then your current project (which is 4 times that size) will cost $400,000 and will take about 8 months to get finished.
Clearly, analogous estimating can be misleading, and they should only be used to give a very fast estimate when a project is being considered in the company (that happens in the pre-selection phase).
Note: Analogous estimating is a top-down estimating technique.