Barlow lenses & Powermates - Do you need either?

What are they? How do you use them? What is the difference? and do you need either?
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*Barlows & Powermates*
Astro Essentials 1.25" 2x Barlow with T thread:
www.firstlight...
Baader Classic Q 2.25x Barlow:
www.firstlight...
BST StarGuider 2x Short Barlow Lens:
www.firstlight...
Celestron Omni 2x 1.25" Barlow:
www.firstlight...
Tele Vue Powermates:
www.firstlight...
StellaLyra ED Deluxe 2x 2" Barlow Lens:
www.firstlight...
ED Deluxe 2x two-inch Barlow Lens
www.firstlight...
*Beginner Telescopes*
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*Telescopes In Stock*
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*Binoculars*
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*I work on the help desk at FLO, However this channel is run in my spare time and it was deemed that there was no conflict of interest*