The 12th house is the house of hidden things, which includes your subconscious mind, your karma and spiritual baggage, and it's the house of endings (since it's the last house). Anything in the 12th house tends to be hidden from us, though we may not know it consciously.
In love, the 12th house brings that same hiding quality, and makes us keep quiet about our feelings, not want to show affection, and hide our hearts.
When you have relationship planets in the 12th house . . .
If you have any natal planets in the 12th house, this can make you someone who hides more than usual in your life. The more planets you have in the 12th house, the more you can hide! And this can stretch out into your relationships, of all types.
Natal Venus in the 12th house can make this your natal way of being in relationships, and you don't want the whole world to see everything. Progressed Venus in the 12th house can make you feel like a native while your progressed Venus is in the 12th house (which can last a few decades!).
When transit Venus is in the 12th house, you can experience a period where you have difficulty showing how you feel, and can stay quiet about any feelings you have for someone. You may want to keep things behind closed doors, under wraps, and may be more prone to something like an affair.
If your natal 5th or 7th house rulers (houses of love and commitment, respectively) are in the 12th house, this can operate similarly the natal Venus in the 12th house. You may keep love and affection quiet with the 5th house, or keep quiet about commitment with the 7th house.
You can come out more under positive aspects (sextiles and trines) to your 12th house cusp or ruler, and it's less hiding and more taking time to be certain of things. But when transit planets are touring your 12th house, you may hide a lot more with everything!
The 12th House & Synastry
When you have a 12th house connection in synastry and your natal planets fall in their 12th house, this can make you have difficulties expressing whatever that planet governs in the relationship (or vice versa if it's their natal planet falling in your 12th house).
This is particularly challenging when it's Venus, the planet of love, and it can be difficult to show love. This can be an issue for both of you when it's planets in the composite 12th house. On the positive, it can show a spiritual connection, but you have to work at expressing yourselves.
1st and 5th house connections can be helpful with that since the 5th house governs affection and the 1st house is an outward, expressive house. In love relationships, you ideally want to see some 5th house connections in synastry and the composite chart to help you show love for one another, and the 1st house can help balance the 12th house since it's out in the open.
Without these to help, it's likely that the relationship never really gets off of the ground.
Suggested Reading: The Love Astrology series:
Mars & Love Astrology
Ceres & Love Astrology
Jupiter & Love Astrology
Saturn & Love Astrology
Uranus & Love Astrology
Neptune & Love Astrology
Pluto & Love Astrology
Chiron & Love Astrology
The 12th House & Love Astrology
The Lunar Nodes & Love Astrology
Eclipses & Love Astrology
Retrogrades & Love Astrology
Asteroids of Your Name & Love Astrology