These are two negative things that no sober Christian wants in his life. But sad to say, we often do, by our careless actions, “grieve” and “quench” the Holy Spirit who dwells in us (Eph. 4:30; 1 Thess. 5:19).
As to quenching the Spirit, God wants to use us as a channel through which He can work for the blessing of others. The Lord said, “He that believeth on Me, as the Scripture hath said, out of his belly shall flow rivers of living water. But this spake He of the Spirit, which they that believe on Him should receive” (John 7:38-39). God desires to work through us by the Spirit, and our responsibility is to allow the Spirit to have that liberty. We must not hinder Him in this. If we do, we are quenching the Spirit. It is like a garden hose that has water running through it, which someone takes and bends together so that the water flow is shut off, or is greatly impeded. Likewise, the Spirit might lead us to do something for the Lord, and our wills are opposed to it, and we don’t do it. Perhaps it is to give out a hymn in a Bible meeting, or maybe to give a gospel tract to someone, etc.
Quenching the Spirit is illustrated in Scripture in the story of Abraham’s servant (Gen. 24). He is a type of the Spirit of God who was sent to secure a bride for Isaac (a type of Christ). It is a picture of the Spirit being sent into this world to call out a bride for Christ. Having gotten permission from Bethuel (Rebekah’s father) to take her to Isaac, her mother and her brother interfered and wanted to detain Abraham’s servant “for a full year” before letting him take her (Gen. 24:55 – margin). This is a picture of quenching the Spirit. The servant then said, “Hinder me not, seeing the Lord hath prospered my way; send me away that I may go to my master” (Gen. 24:56). Likewise, the Spirit is saying to us, “Hinder Me not.” He wants to lead our hearts after Christ and use us as a channel of blessing to others, and He doesn’t want anything to come in the way of that.
Grieving the Holy Spirit is slightly different. It has to do with us going out and doing something that the Spirit has not led us to do, whereby He is grieved by our actions. It is sin that grieves the Spirit. When the believer sins, the divine Guest within feels it and will exercise us to judge it.
Simply put; quenching the Spirit is not doing something He would have us to do, and grieving the Spirit is doing something that He hasn’t led us to do.