It's kinda hard to talk about meta in FGO, because we don't have PvP here. We do need to stretch the definition a little, but there are some units that stand out as being more widely applicable than others, and I'll try to explain as briefly as possible who they are and why I consider them to be so.
First of all, FGO has 2 major fronts: farming and Challenge Quests. Farming refers to the capability of obtaining resources from events or free quests. The "meta" here is to complete the missions as fast as possible - usually within 3 turns - so that we can obtain the resources we need as fast as possible. Example: there's a mission you need to clear to buy all the materials from an event shop. Doing it with team A takes 3 turns and a total of 2 minutes per run. Team B takes 4 turns and 3 minutes per run. If you only clear the mission once or twice, the difference will be negligible, but if you clear it 50x it will be noticeable, especially of you use a macro to automate your farming.
The second front refers to boss fights in general. You encounter them in the main story and usually at the end of events. Here it's simpler, whether you have the team and/or strategy to beat them or not.
Now, where do the "meta" units come in? They come into play because the most efficient and effective way to clear both farming and hard content is to build a team with 1-2 DPSs and 2-3 supports. Sometimes you'll need to get creative, and by no means is this the only way to clear, but most content can be done with the aforementioned team composition, and here's the thing: your DPSs change accordingly to the enemy classes, but the supports don't. The "meta" is to match your DPSs NP type with supports that can buff that specific type. Here's the short list. I'll let others in the comments complement this list.
Buster Units
Boss Fights: Merlin
Farming: Koyanskaya of Light, Oberon
Arts Units
Boss Fights: Lady Avalon, Tamamo no Mae, Artoria Caster
Farming: Artoria Caster
Quick Units
Boss Fights: no one, unfortunately
Farming: Scáthach-Skadi (Caster), Scáthach-Skadi (Ruler)
Generic
Boss Fights: Reines, Waver, Van Gogh
Farming: Oberon
This doesn't mean you can't take, say, Merlin, to a farming quest, it's just not his most adequate role. Also, do take note that Quick Units don't really have an amazing support for challenge quests. This is because both Skadis provide plenty of offensive buffs, but very little defensive utility. This is an argument to claim that Quick Units are weaker in the meta than buster units, but it doesn't mean that Quick Unit's are incapable of doing the job for you.
Hope this helps.
