A translation or slide involves moving a figure in a specific direction for a specific distance. Vectors are often used to denote translation, because the vector communicates both a distance (its length) and a direction (the way it is pointing).
The vector shows both the length and direction of the translation.
A glide reflection is a combination of two transformations: a reflection over a line, followed by a translation in the same direction as the line.
Reflect over the line shown; then translate parallel to that line.
Only an infinite strip can have translation symmetry or glide reflection symmetry. For translation symmetry, you can slide the whole strip some distance, and the pattern will land back on itself. For glide reflection symmetry, you can reflect the pattern over some line, then slide in the direction of that line, and it looks unchanged.
The patterns must go on forever in both directions.