Soak apricots in boiling water in a bowl until hydrated, about 30 minutes. Blend apricots, remaining water, and vanilla extract in a food processor, working in batches, until blended but still slightly chunky.
Combine apricot mixture with pectin in a large pot over medium heat; cook until just boiling. Add sugar and lemon juice; boil until sugar has dissolved, 1 to 2 minutes.
Sterilize jars and lids in boiling water for at least 5 minutes. Pack the apricot jam into the hot, sterilized jars, filling the jars to within 1/4-inch of the top. Run a knife or a thin spatula around the insides of the jars after they have been filled to remove any air bubbles. Wipe the rims of the jars with a moist paper towel to remove any food residue. Top with lids, and screw on rings.
Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil, then carefully lower the jars into the pot using a holder. Leave a 2-inch space between the jars. Pour in more boiling water if necessary until the water level is at least 1 inch above the tops of the jars. Bring the water to a full boil, cover the pot, and process for 10 minutes.
Remove jars from the stockpot and place onto a cloth-covered or wood surface, several inches apart, until cool, about 1 hour. Once cool, press the top of each lid with a finger, ensuring that the seal is tight (lid does not move up or down at all). Store in a cool, dark area.