Hit dice don't actually affect your hits
Hit dice do affect your ability to survive hits. The name originally referred to the dice you might roll to determine your hit point maximum, and in 5th edition it also describes a healing mechanic.
Here's the lore on why it's called that.
In the miniature wargames that inspired D&D, when two squads or units of men fought, you rolled dice to determine how many of the enemy minis were killed. Each was one "hit", and a strong or lucky unit might deal several simultaneous hits to an enemy unit.
Chainmail (1971), a wargame by D&D creator Gary Gygax, introduced hero characters (meant to represent characters like Legolas or Gimli), who fought as effectively as an entire unit of men on their own. Hit points did not exist, so heroes could not be killed unless they took a certain number of simultaneous hits.
Original Dungeons & Dragons (1974) introduced the notion that characters might instead be killed by cumulative hits, a concept we today know as hit points. You rolled dice (originally 1d6) at character creation and each time you leveled up to determine how many hit points your character could take. This was known as dice for cumulative hits, or later hit dice.
This remained the status quo in D&D until about D&D 4th edition (2008), which made game balance a priority. Designers decided that rolling randomly for your hit point total was too unbalanced, since a few lucky or unlucky rolls could make your character extremely strong or weak for their level. The standard method was now taking average of your hit dice rounded up, so that a character who might gain 1d8 hit points upon levelling up would simply gain 5.
D&D 5th edition (2014) sought a return to tradition. Hit dice returns to its original meaning, although you automatically have maximum at first level (e.g. your rogue will always have 8 + Con modifier hit points at first level, rather than 1d8), and each time you level up you can still choose to take the average rounded up (e.g. you can gain 1d8 + Con modifier to your hit point maximum, or 5 + Con modifier).
Slightly confusingly, hit dice are now also used as a separate mechanic for healing during short rests between combat.
This harkens back to the healing surge mechanic of 4th edition which sought to remove the reliance on cleric spells for healing between combat, since in 3rd edition clerics were often treated like a healing battery. The healing surge in turn derives from the reserve points 3rd edition variant used in designer Mike Mearls' Iron Heroes, a low-magic D&D variant without clerics, so player characters needed some ability to heal themselves between fights.
Essentially, hit dice in 5th edition are now a reserve of healing equal to the dice you would roll if you rolled randomly for hit points, which you don't actually do at first level any more for balance reasons.
With regards your attacks, your character would roll 1d20 + 5 with both daggers to see if they hit, dealing 1d4+3 damage on a successful hit with the primary weapon, and 1d4 on a hit with the secondary weapon. In the Player's Handbook, see p.194-196 for the rules on attack rolls, melee attacks, two-weapon fighting and damage, and p.186 for the rules on spending hit dice to heal.