You can use Spatial Join to determine how many points are within each polygon. The output polygon feature class will have two new fields added (Join_Count and TARGET_FID). Join_Count indicates how many join features match each target feature (TARGET_FID). Then you can select by attribute those that have 3 or more.About joining and relating tablesYou can also right click the polygon layer in ArcMap > Joins and Relates > Join. Select the option to Join Data From Another Layer Based Upon Spatial Location. Then choose the points layer to join to. The output feature class will contain a count field for each polygon.