Meiosis leads to half chromosome number reduction. In diploid organisms, this leads to haploid cells formation. But what could occur from triploids? What would be the resulting ploidy? And from tetraploidy? Could a tetraploid organism produce diploid gametes without any meiosis dysfunction?
If an organism is triploid, the resulting gametes will be aneuploid. Basically, for each set of 3 chromosomes it has to divide unevenly into the gametes. Some will get 1 chromosome, others 2. And that's true for every set of chromosomes. It's mathematically possible, but very very rare to create a gamete with exactly 1 copy of each chromosome (or exactly 2 copies of each chromosome). That's why triploid organisms are infertile.
Tetraploid organisms are usually fully fertile.
Most genetics textbooks, especially those with a plant focus, will have some nice diagrams to illustrate these possibilities.
For triploids, the fundamental problem is pairing issues during the long prophase I of meiosis when homologous chromosomes should form bivalents. Some plants are able to get round this by forming trivalents or a bivalent and a univalent. It would seem plants are better at dealing with the meiotic consequences of polyploidy than animals.
See this hyperlink for further details:
https://www.nature.com/scitable/popular-discussion/703
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