Strange icon in Word prevents proper text alignment

Solution 1:

Those icons should indicate that your cursor is within a table cell, and these represent the locations of the vertical boundaries between columns. Moving these resizes the columns, so some text in the cell may be obscured if it no longer fits inside.

Note that the table may not have actual lines drawn at these boundaries. Turn on "Show non-printing characters" to see some of the table-specific stuff in the document.

If you don't need the table and just somehow ended up with one (either by accident, or because you're using a document you received from someone else), just grab the text from the table and copy it outside for everything to behave as usual (then select and delete the table).