Arsthbt

I am guessing it represents the stretch of notes to be played at the changed tempo, and begin playing at the initial tempo after that.

Edit from the comments: The piece is for playing guitar using plectrum.

This line refers to the I, not to the "Allegro".

As OP mentioned in the comments, the I stands for the first position, i. e. the first fret on the guitar. So the line means, that all notes under it have to be played in the first position.

Not associated with the time change, just coincidental. On guitar music, there's often a Roman numeral printed to suggest a good position on the neck to play that section. Here, it's the scale of the F Mixolydian mode, starting from 1st fret bottom string. So a sensible position to play all the notes would be starting o that very fret. Although, promoting an open A on the 5th string somewhat negates the 'I'. Not a lot of point in putting it, in my opinion.

That looks like guitar music (single staff, G clef, Arabic numbers that make sense for guitar fingerings). If so...

It gives you the position that passage is to be played in

The Bb note in the preceding measure can't be played on any of the five lowest frets. Given the fingering for that note and the ones that follow, the music is indicating third position there: G with the first finger/3rd fret, Eb ad Ab with the second finger/4th fret, F and Bb with the fourth finger/6th fret.

There's no finger number indicated for the Eb at the start of the measure you're questioning. But the second note, F below the staff, can't be played in third position, so it's going to require a shift. The music is telling you to shift ON the F, rather than shifting earlier in preparation for the F.

Guitar positions are traditionally marked with Roman numerals. That F is playable in either first or second position - the music is telling you to do it in first.

Position marks are usually preceded with "C" (Italian for capotasto, fret) to avoid confusion with Roman numerals from analysis. But not all publishers do that.

The horizontal line tells you all the notes under it are to be played in first position. It ends at the Bb; the C that follows could be played in either first or second position, so it's your choice.

As a guitarist, it's a little odd that the publisher chose to mark the position for that passage. Since there aren't many choice for how to play the F, and they also provide finger numbers, it's already obvious that passage is in first position. And they didn't mark the measure below - from the fingering, beat 1 is first position, beats 2 & 3 are second position, and beat 4 is fourth position. But sometimes publishers/composers do odd things.