Pot Odds relate the profit you may get with the probability of completing your hand.
Let's try to explain what Pot Odds are with a practical example:
In a set of 5 cards that includes Ace, King, Queen, Jack and 10, we pick a card randomly and every time an Ace comes out we win 5€, if any other card comes out we lose 1€. Since the probability of getting an Ace is of 1 in 4, every 5 times we play we should get 1 Ace. Every time another of the other 4 cards comes out we lose 1€, which means that every 5 times we play we should win 5€ and lose 4€ and have a profit of 1€. In the long run these odds are, therefore, favourable.
This simple logic can also be applied to Poker.
So let's have a look at a Poker example:
This is your hand:
Flop:
Now imagine there are only 2 players left in the pot: you and an opponent. There are 80€ in the pot and your opponent bets 20€. What should you do?
First you should calculate the probability of getting another clubs card to complete your flush.
We know 5 of the 52 deck cards, the ones in our hand and the flop cards. There are 47 left, 9 of which are clubs. Therefore, the odd of getting a clubs card is 9:38, approximatelly 1:4.
Once you've calculated the odds of getting the card you need, it's time to see if the Pot Odds are favourable to call. Your opponent has bet 20€ in a 80€ pot, so the pot is now at 100€.
Therefore, the Pot Odds are at 20:100, or 1:5. Therefore, you should call, since the odds you get from the pot are better than the odds to complete your flush with the next card.
In the long run, you'll win more money than you'll lose, since in 5 plays you'll lose 4 in a total of 80€ (20€ each time), but you'll win 100€ once in 5 plays. This means you'll get a profit of 20€ every 5 matches.
You should call every time the Pot Odds are more favourable than the odds of getting the card you need.
There are many tables available with the odds of getting the cards you need (card odds). They usually indicate the number of favourable cards (outs) that you may get to complete your hand and the odds of getting it. Here's an example you may find on the internet.
Outs

PreFlop 
Turn 
River 
Example 
20

67.5% 
42.5% 
43.5% 

19

65% 
40.4% 
41.3% 

18

62.4% 
38.3% 
39.1% 

17

59.7% 
36.2% 
36% 

16

57% 
34% 
34.8% 

15

54.1% 
31.9% 
32.6% 
Straight or Flush: for a straight you need a 2 or a 7, for a flush there are 9 cards available 9+3+3=15
(the 2 and the 7 should only be accounted for once) 
14

51.1% 
29.8% 
30.4% 

13

48.1% 
27.7% 
28.2% 

12

45% 
25.5% 
26.1% 
Straight or Flush: for a straight you need a 7, for a flush there are 9 cards available 9+3=12
(the 7 should only be accounted for once) 
11

41.7% 
23.4% 
23.9% 

10

38.3% 
21.3% 
21.7% 

9

35% 
19.1% 
19.6% 
You need a card to complete the flush: there are 9 available in the deck 
8

31.4% 
17% 
17.4% 
To complete the straight you need 3 4 5 or 6
2 and 7 will do (4+4=8) 
7

27.8% 
14.9% 
15.2% 

6

24.1% 
12.8% 
13% 
You have an AK hand
there are 3 Aces + 3 Kings left = 6 
5

20.3% 
10.6% 
10.9% 

4

16.5% 
8.5% 
8.7% 
Only a 5 will complete your straight
there are 4 cards left in the deck 
3

12.5% 
6.4% 
6.5% 

2

8.4% 
4.2% 
4.3% 

1

4.2% 
2.1% 
2.2% 

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