On Shabbat, a friend asked me if there was any connection between the word miluim מילואים used in describing the construction and service in the tabernacle (mishkan) and the word miluim used in modern Hebrew for the army reserves.

Well, there certainly is a connection, but it isn't so obvious. Let's take a look.

The word is the gerund form of the root מלא, meaning "to fill" or "to be full", and is only found in the plural. It appears in two separate contexts. The first (Shemot 25:7; 35:9, 27) describe the settings of the stones in the ephod and the breastpiece - אבני מלאים - avnei miluim. Daat Mikra, following Rashi (on 25:7), says that these gems fill the grooves in the gold (or other material), so they are literally "filling stones". The Ramban disagrees, and following Onkelos, focuses on a different sense of the root מלא - "full, complete, perfect". He writes (Chavel translation):

But the sense of the word milu'im is that the stones be whole as they were created, and that they should not be hewn stones which were cut from a large quarry or from anything which has been chipped off. ... This is why Onkelos translated [avnei milu'im - avenei] ashlamutha (stones of perfection).

The other use of milium in the Torah is for the initiaton, inauguration or consecration of the kohanim (priests), as mentioned in Shemot 29:22,26,27,31,34 and Vayikra 7:37;8:22,28,29,31,33. Levine, in the JPS commentary on Vayikra 8:22, where the איל המלאים ail hamilium - "ram of ordination" is discussed, writes:

The Hebrew term millu'im, "ordination," literally means "filling" the hands, a symbolic act that transfers or confers status or office. Further on, in verses 27-29, we read that parts of the offerings were actually placed on the palms of Aaron and his sons, who raised them in a presentation to God. The biblical formula mille' yad, "to fill the hand," is limited to the appointment of priests and cultic officials.