Standard english would be the one that is spoken or written across different english speaking areas, with a standard spelling, pronunciation, grammar etc.
Non-standard englishes would have local variations in pronunciation or spelling or lexicon etc.
So compare for instance english as spoken by scottish or irish people to the english you would hear on the BBC world service. It might sound different, have different vocabulary, maybe some variations in syntax ("I'm after going to the pub") etc. It might be harder for an australian or indian english speaker to understand, but for all that it's still english.
The BBC variety would seem clear and normal to english speakers from pretty much anywhere. The Standard variety of a language also tends to have more prestige. it's the one taught in school, the one books are usually published in and so on. Get on youtube or project gutenberg and look for stuff from different englishes.