I'm looking at the Spell Slots per Spell Level for bard at 14th level.  It says that the bard has 18 known spells, 4 Cantrips, and 17 spell slots (4-1st, 3-2nd, 3-3rd, 3-4th, 2-5th, 1-6th, 1-7th). As a bard, there is no spell book. They just innately know their spells to prepare for the day, like priests.  So when you level up from level 13 to 14 level in bard, at 13th level you had 16 known spells and the same 17 spell slots as 14th level bard. 

So my question is, when I get 2 more spells to learn, when I level up from 13th level bard to 14th level bard, are the 2 new spells restricted to specific levels or can these two new learned spells of any level?

Quote from DamianKnight >>

I'm looking at the Spell Slots per Spell Level for bard at 14th level.  It says that the bard has 18 known spells, 4 Cantrips, and 17 spell slots (4-1st, 3-2nd, 3-3rd, 3-4th, 2-5th, 1-6th, 1-7th). As a bard, there is no spell book. They just innately know their spells to prepare for the day, like priests.  So when you level up from level 13 to 14 level in bard, at 13th level you had 16 known spells and the same 17 spell slots as 14th level bard. 

So my question is, when I get 2 more spells to learn, when I level up from 13th level bard to 14th level bard, are the 2 new spells restricted to specific levels or can these two new learned spells of any level?

In general (NOT for level 14; see below for more), the rule is:

The Spells Known column of the Bard table shows when you learn more bard spells of your choice. Each of these spells must be of a level for which you have spell slots, as shown on the table. For instance, when you reach 3rd level in this class, you can learn one new spell of 1st or 2nd level. Additionally, when you gain a level in this class, you can choose one of the bard spells you know and replace it with another spell from the bard spell list, which also must be of a level for which you have spell slots.

So in general, when you level up, you learn additional spells which must be at least level 1 and at most of a spell level you have slots for (you have the slots of the new level for determining this).  Likewise, in general, these new spells are chosen from the Bard spell list, which may be different for you than for other Bards, based on subclass, race, feats, or whatever.

However, Bards do not accurately list their spells known:

By 10th level, you have plundered magical knowledge from a wide spectrum of disciplines. Choose two spells from any classes, including this one. A spell you choose must be of a level you can cast, as shown on the Bard table, or a cantrip. The chosen spells count as bard spells for you and are included in the number in the Spells Known column of the Bard table. You learn two additional spells from any classes at 14th level and again at 18th level.

This means for your specific question, level 14, you get both of these:

1. You can drop any 1 Bard spell you know and replace it with a Bard spell you have the slots for, like with any Bard level.  This means the new spell is min level 1, max level 7.
2. You get 2 spells which can be from any spell list and which can be cantrips.  They still can't be of a higher level than you have slots for, so both can be max level 7.

That all make sense?