A simple example:
Current equity of $100B, 100 shares outstanding. Each share is worth $1B, with 1% of voting power.
Then we issue $10B of equity via 10 shares.
Now we have equity of $110B, with 110 shares outstanding. Each share is still worth $1B, except each share now has 1/110 of voting power, instead of 1/100. Each share now only controls 0.91% of the company. Their ownership has been diluted.
Buyback example:
There are 10 shares of ABC Corp, it has a market cap of $100. Each share is worth $10.
ABC corp buys back one share and destroys it, leaving 9 shares.
$100/9 shares=$11.11 per share.
Dilution example:
There are 10 shares of ABC Corp, it has a market cap of $100. Each share is worth $10.
ABC corp needs $10 so they sell one additional share which the board has authorized. There are now 11 shares.
$100/11 shares=$9.09
In summation, a buyback increases the value of each share and issuing more stock reduces the value of each share.