Byleth's D-Tilt is a combo starter and neutral tool. In neutral, it can be used to space on shield, and to call out grounded approaches. It is Byleth's longest ranged tilt attack, and as such can be used when other tilt attacks won't reach. However, when at max spacing, down tilt generally won't combo on DI out. D-Tilt is only safe when spaced, and is also Byleth's slowest tilt, so don't use it repeatedly on shield.
It also has the ability to low-profile some attacks. This is most notable against rising aerials, or attacks that hit high such as Sephiroth F-Air.
Some notable uses of D-Tilt include:
Catching landings: The long hitbox can cover a good area of the ground at once to catch someone landing near you and send them back in the air.
Pivot D-Tilt: Pivot Cancel D-Tilt caused D-Tilt to slide. This can be used to catch people overshooting out of a back dash, or used as an approach tool.
Parry punish: D-Tilt can punish most moves that are -11 or worse out of parry, which allows you to start a combo or kill confirm them after the parry.
Corner Pressure: Due to how large it is and how much it low profiles, it's a fantastic tool to both help you get out of the corner or to pressure an opponent in the corner.
D-Tilt combos:
D-Tilt > U-Tilt
D-Tilt > F-Tilt
D-Tilt > U-Air
D-Tilt > N-Air
D-Tilt > DIDJ N-Air
D-Tilt > Up-B
D-Tilt > U-Air is a common kill confirm. To see kill percents as of 7.0.0, see the D-Tilt -> U-Air Percents graphic.
D-Tilt can notably also combo into F-Air and U-Smash if done from a two-frame or hitting ledge hang.