As far as jEdit is concerned, a "paragraph" is a block of text enclosed with double-newlines. This is also how TeX defines a paragraph. Note that jEdit doesn't parse HTML files for "<P>" tags, nor does it support paragraphs delimited only by a leading indent.
You can move the caret a paragraph at a time by holding down Control in addition to Up or Down. Paragraphs can be selected if you hold down Shift in addition to Control.
Edit>Selection>Select Paragraph (keyboard equivalent: Control-E P) will select the paragraph containing the caret. Edit>Paragraphs>Delete Paragraph (keyboard equivalent: Control-E Control-D) will delete the paragraph containing the caret.