Vectors are arrows that point in a certain direction and have a certain length. Longitudinal vector fields are a bunch of these arrows that are all pointing in the same direction as the field.
Think of them like a field of corn that all grows in the same direction. If you walk through it, all the stalks will be pointing in the same way, like a bunch of arrows pointing in the same direction.
Transverse vector fields, on the other hand, have arrows pointing in different directions. Think of a field of sunflowers that are all growing at different angles.
If you walk through this field, the sunflowers will all be facing different directions, like a bunch of arrows pointing in different directions.
So, to sum up: longitudinal vector fields have arrows pointing in the same direction, like a field of corn. Transverse vector fields have arrows pointing in different directions, like a field of sunflowers.